Partial Frobenius algebras, which arise in our characterisation of DCR categories, are special/separable Frobenius algebras without units. The version with units was originally studied in [1]}, is deeply connected to the relational algebra [2]}, characterises 2-dimensional TQFTs [3]}, and has been used extensively in categorical approaches to the study of quantum information and quantum computing, such as the ZX calculus [4]}. In a similar way to the use of partial Frobenius algebras in this paper, they are used in the recently proposed Frobenius theories [5]}, which are algebraic theories that take their models in the category of relations \(\mathsf {Rel}\) , and are guided by the structure of cartesian bicategories of relations [1]}.
